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Abstract:
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This work first introduces a novel elastic time distance for sparse multivariate functional data, which serves as a foundation for clustering functional data with various time measurements per subject. Then it introduces a robust two-layer partition clustering. With our proposed distance, our approach, besides being applicable to both complete and imbalanced multivariate functional data, is outlier-resistant and can detect outliers that do not belong to any clusters. Furthermore, classical distance-based clustering methods such as K-medoids and agglomerative hierarchical clustering are extended to the sparse multivariate functional case based on our proposed distance. Numerical experiments on simulated data highlight the excellent performance of the proposed algorithm compared to existing model-based and extended distance-based methods. Using Pacific Northwest cyclone track data as a motivating example, we demonstrate the effectiveness of the proposed approach.
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